{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline --no-import-all\n",
    "from scipy.stats import chi2, norm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "xmin=-5\n",
    "xmax=5\n",
    "reals = np.linspace(xmin,xmax,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def f1(x):\n",
    "    return np.exp(-0.5*(x)**2)/np.sqrt(2*np.pi) \n",
    "    \n",
    "def f2(x):\n",
    "    return np.exp(-x)/(np.exp(-xmin)-np.exp(-xmax))\n",
    "\n",
    "dists = [f1,f2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "q = lambda h: (lambda x: np.sqrt(h(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def inner_product(q1,q2, xmin=xmin, xmax=xmax):\n",
    "    # this is a simple numeric integration\n",
    "    num = 50000.\n",
    "    xarray = np.linspace(xmin,xmax,num)\n",
    "    return np.sum(q1(xarray) * q2(xarray),dtype=np.double)*(xmax-xmin)/num"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1056ab550>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "k3AHRDwZOkgDnMKGlUpZVu5gtqGBsiStFdgPd/R1XvwQ+BpuKjNvdsAdL/Iz3NlEr8Ad51BWtQOC\n",
       "6nUX7s+5zr7hX2sAbp5nNG6EXsfV21Ohq89vCu58Jh2yeF6ZSp/feWwY8XwDd8DSdY0KlaCiHFm4\n",
       "BW6u9Su4A8zy4F9w59qZiztEP2+acSsAz8SdNuFS3F+L54cMBXAH7kChDotxh1PnwV64A6CW+m0N\n",
       "7vw02wXMlISTgNm4oxnzYAwbT61MIX87PFtwJ746K3SQmF2E+2tqKe5Eau8CVwdNFK8huM+twzjc\n",
       "aTeCmwx809/eFXgxYJak5XGOvB23+mFQ6CAxquWAtyyLcOX2w9BBEnYw+ZsjB3flrV39bUNKVvq1\n",
       "AL/EndDpMfL551CH58hfkS/CnSd8rt9+EjZObMod8JYX43Dzx0+w4fvW3uX/kU0Hk89VK/vgplXy\n",
       "tuRXREREREREREREREREREREREREREREREREpNj+H5DXzpSCj+fRAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1056ab490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(reals,dists[0](reals))\n",
    "plt.plot(reals,dists[1](reals))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1056daf10>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "FPgV/8bVPH4ev/BOGazN/EX/pwNz8NP3vxIwUx72Ae4BFgmcIytjWLBrZRLlu+DZBtwC/Ch0kIyd\n",
       "hH83NR2/BMCHwO+CJspWx25RHTYBbgyUZQEHAD9L76+GX6+krMrYRz4BP/phqdBBMtTIhLciS/DF\n",
       "7czQQXI2jvL1kYNfMXW19L4jkpF+bcDv8TuJP0Q53w51eIHyFfKp+DVoHknbeWHjZKarCW9lsQm+\n",
       "//hR5v+/TVjoVxTTOMo5amVdfLdK2Yb8ioiIiIiIiIiIiIiIiIiIiIiIiIiIiIiIiFTb/wfztoY7\n",
       "48xLQQAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1056da0d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(reals,q(dists[0])(reals))\n",
    "plt.plot(reals,q(dists[1])(reals))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "t = 0*np.arccos(inner_product(q(dists[0]),q(dists[1])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "test 4.98355890935e-06 1.0\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0.0064145249130260727, 0.99997942700561182)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dot01 = inner_product(q(dists[0]),q(dists[1]))\n",
    "t1 = lambda x: q(dists[1])(x) - dot01*q(dists[0])(x)\n",
    "norm1 = inner_product(t1,t1)\n",
    "u1 = lambda x: t1(x)/np.sqrt(norm1)\n",
    "#unnorm_tan = lambda x: u1(x)*normedBaryCoords[0]+u2(x)*normedBaryCoords[1]\n",
    "#norm_tan = inner_product(unnorm_tan,unnorm_tan)\n",
    "#tangent = lambda x: unnorm_tan(x) / np.sqrt(norm_tan)\n",
    "tangent = u1\n",
    "print 'test', inner_product(q(dists[0]),tangent), inner_product(tangent,tangent)\n",
    "q_interpolant = lambda x: np.cos(t)*q(dists[0])(x) + np.sin(t)*tangent(x) \n",
    "interpolant = lambda x: ( np.cos(t)*q(dists[0])(x) + np.sin(t)*tangent(x) )**2\n",
    "np.arccos(inner_product(q(interpolant),q(dists[0]))),inner_product(q(interpolant),q(interpolant))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.99997942700561182, 1.0000800124137632, 1.3331268554450413)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inner_product(q(dists[0]),q(dists[0])), inner_product(q(dists[1]),q(dists[1])), np.arccos(dot01)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x109807890>]"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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       "UjsMvGxrRZHVFfOz1ZiAWXbDdrcCvw/eHsjxa6EkmkQcI5+Kmf2Qa3chEdSUE97imYUJt/+xu5Ao\n",
       "m0jijZGDufJWzdIDPhwy0y8F+CdmQacvScyPQzW2kHhBvgnYjvkouwqzjnkiCHXCW6KYgBk/Xk3t\n",
       "321qg/8iPk0kMWetjMAMqyTalF8hhBBCCCGEEEIIIYQQQgghhBBCCCGEEEIIIYQQQgghktv/Bz8j\n",
       "9G25zVsXAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x108c66d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(reals,.01+dists[0](reals))\n",
    "plt.plot(reals,.01+dists[1](reals))\n",
    "t = 0*np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "plt.plot(reals,interpolant(reals))\n",
    "t = 0.75*np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "plt.plot(reals,interpolant(reals))\n",
    "t = 1*np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "plt.plot(reals,interpolant(reals))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10011127257427471"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "/BjwM9xkjlcC/ytkqDS3AOfW3N+EO4OtDE7FnXbdfwbfftz8PMcGzJS1DwLLcTNllsF0Dm7RLKZ8\n",
       "A61dwG3An4cOkoNrcN/AtuJmYn0B+H9BE2VnAu7n6jcb+FGgLA1bCHzW334D8FjALHkrWw9+Hu5o\n",
       "jLGhg2So7CfpJbiC98XQQdrgXMrVgwe4B1cnAZYQwVGHXcC3cBexeJDyfa2qtYVyFfiNwH/gvg6v\n",
       "Br4SNk5mynyS3mxcb3oNB/7d5gVNlJ9zKd9RNKfj2jNlOzRZRERERERERERERERERERERERERERE\n",
       "RERERMro/wO8+32FZZWsBwAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10986fe90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = .1*np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "plt.plot(reals,interpolant(reals))\n",
    "np.arccos(inner_product(q(interpolant),q(dists[0])))/np.arccos(inner_product(q(dists[0]),q(dists[1])))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x109d1d7d0>]"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "/AAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109d1df10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "distarray = np.zeros(30)\n",
    "tarray = np.linspace(0,np.arccos(inner_product(q(dists[0]),q(dists[1]))),30)\n",
    "for i,tt in  enumerate(tarray):\n",
    "    t=tt\n",
    "    distarray[i] = np.arccos(inner_product(q(interpolant),q(dists[0])))/np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "plt.plot(tarray,distarray)\n",
    "plt.plot([0,np.arccos(inner_product(q(dists[0]),q(dists[1])))],[0,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "mixture = lambda x: (1-tmix)*dists[0](x) + (tmix)*dists[1](x) \n",
    "unnormcox = lambda x: dists[0](x)**(1-tcox) * dists[1](x)**tcox\n",
    "cox = lambda x: unnormcox(x)/inner_product(q(unnormcox),q(unnormcox))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x109d58e90>]"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "Q2Hvwyn4ipnJ+OHwlaqh96Ib8BieJybjxeZKdS9eW/gR/+3tcFpu3hQRERERERERERERERERERER\n",
       "ERERERERERGRcvD/AWI9xWmo5HpZAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109cddb50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ntsteps=100\n",
    "interpolant_distarray = np.zeros(ntsteps)\n",
    "mixture_distarray = np.zeros(ntsteps)\n",
    "cox_distarray = np.zeros(ntsteps)\n",
    "\n",
    "tarray = np.linspace(0,1,ntsteps)\n",
    "for i,tt in  enumerate(tarray):\n",
    "    t=tt*np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "    interpolant_distarray[i] = np.arccos(inner_product(q(interpolant),q(dists[0])))/np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "    tmix = tt\n",
    "    mixture_distarray[i] = np.arccos(inner_product(q(mixture),q(dists[0])))/np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "    tcox = tt\n",
    "    cox_distarray[i] = np.arccos(inner_product(q(cox),q(dists[0])))/np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "\n",
    "plt.plot(tarray,interpolant_distarray)\n",
    "plt.plot(tarray,mixture_distarray)\n",
    "plt.plot(tarray,cox_distarray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def eta_cox(tt):\n",
    "    return tarray[np.argmax(cox_distarray>tt)]\n",
    "def eta_mixture(tt):\n",
    "    return tarray[np.argmax(mixture_distarray>tt)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x109f883d0>]"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "DNwAAAAASUVORK5CYII=\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109cb9550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "temp = np.zeros(ntsteps)\n",
    "for i, tt in enumerate(tarray):\n",
    "    temp[i]=eta_cox(tt)\n",
    "plt.plot(tarray,temp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10a0f1dd0>]"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "RERERERERERERERERERERERERERERKQy+D8gkfdhWJbngQAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109f88f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "interpolant_etaarray = np.zeros(ntsteps)\n",
    "cox_etaarray = np.zeros(ntsteps)\n",
    "mixture_etaarray = np.zeros(ntsteps)\n",
    "\n",
    "for i,tt in  enumerate(tarray):\n",
    "    t=tt*np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "    interpolant_etaarray[i] = np.arccos(inner_product(q(interpolant),q(dists[0])))/np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "    tmix = eta_mixture(tt)\n",
    "    mixture_etaarray[i] = np.arccos(inner_product(q(mixture),q(dists[0])))/np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "    tcox = eta_cox(tt)\n",
    "    cox_etaarray[i] = np.arccos(inner_product(q(cox),q(dists[0])))/np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "\n",
    "plt.plot(tarray,interpolant_etaarray)\n",
    "plt.plot(tarray,mixture_etaarray)\n",
    "plt.plot(tarray,cox_etaarray)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Library/Python/2.7/site-packages/IPython/kernel/__main__.py:8: RuntimeWarning: invalid value encountered in arccos\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10a2697d0>]"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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       "JG1nAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109cd4ed0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cox_interp_dist = np.zeros(ntsteps)\n",
    "mixture_interp_dist = np.zeros(ntsteps)\n",
    "\n",
    "for i,tt in  enumerate(tarray):\n",
    "    t=tt*np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "    tmix = eta_mixture(tt)\n",
    "    tcox = eta_cox(tt)\n",
    "    cox_interp_dist[i] = np.arccos(inner_product(q(interpolant),q(cox)))\n",
    "    mixture_interp_dist[i] = np.arccos(inner_product(q(interpolant),q(mixture)))\n",
    "\n",
    "plt.plot(tarray,mixture_interp_dist)\n",
    "#plt.plot(tarray,cox_interp_dist)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "8MEHH3zwwQcffPDBBx988MEHH3zwwQcffPDBBx988MEHH3zwwQcffPDBBx988MEHH3zwwQcffPDh\n",
       "ysb/ARdPi4nQv3WjAAAAAElFTkSuQmCC\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109e4a1d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(reals,dists[1](reals)+.01,ls='solid')\n",
    "for i,tt in  enumerate(np.linspace(0,1,30)):\n",
    "    t=tt*np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "    tmix = eta_mixture(tt)\n",
    "    tcox = eta_cox(tt)\n",
    "    #plt.plot(reals,mixture(reals))\n",
    "    #plt.plot(reals,interpolant(reals), ls='dotted')\n",
    "    plt.plot(reals,cox(reals),ls='dashed')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "WCwWi8VisVgsFovFYrFYLBaLxWKxWP6/+R+ofJMzwDkDcgAAAABJRU5ErkJggg==\n"
      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10a3d0950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(reals,dists[1](reals)+.01,ls='solid')\n",
    "for i,tt in  enumerate(np.linspace(0,1,30)):\n",
    "    t=tt*np.arccos(inner_product(q(dists[0]),q(dists[1])))\n",
    "    tmix = eta_mixture(tt)\n",
    "    tcox = eta_cox(tt)\n",
    "    plt.plot(reals,mixture(reals))\n",
    "    #plt.plot(reals,interpolant(reals), ls='dotted')\n",
    "    #plt.plot(reals,cox(reals),ls='dashed')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "def dbydt(q1, tarray, xmin=xmin, xmax=xmax):\n",
    "    # this is a simple numeric integration\n",
    "    num = 50000.\n",
    "    xarray = np.linspace(xmin,xmax,num)\n",
    "    temp = np.zeros(tarray.size)\n",
    "    counter = 0\n",
    "    for t1, t2 in zip(tarray, np.roll(tarray,1)):\n",
    "        t,tcox,tmix=t1,t1,t1\n",
    "        q1array = q1(xarray)\n",
    "        t,tcox,tmix=t2,t2,t2\n",
    "        q2array = q1(xarray)\n",
    "        temp[counter] = np.sum(q1array * q2array,dtype=np.double)*(xmax-xmin)/num\n",
    "        counter+=1\n",
    "    return temp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# this is a simple numeric integration\n",
    "num = 50000.\n",
    "xarray = np.linspace(xmin,xmax,num)\n",
    "mixture_velocity = np.zeros(tarray.size)\n",
    "cox_velocity = np.zeros(tarray.size)\n",
    "interpolant_velocity = np.zeros(tarray.size)\n",
    "counter = 0\n",
    "for tt, ttt in zip(tarray, np.roll(tarray,1)):\n",
    "    t,tcox,tmix=tt,tt,tt\n",
    "    #q1array = q(cox)(xarray)\n",
    "    q1array = np.sqrt(cox(xarray))\n",
    "    t,tcox,tmix=ttt,ttt,ttt\n",
    "    #q2array = q(cox)(xarray)\n",
    "    q2array = np.sqrt(cox(xarray))\n",
    "    #print np.sum(q1array-q2array), 'test'\n",
    "    cox_velocity[counter] = np.arccos(np.minimum(1.,np.sum(q1array * q2array,dtype=np.double)*(xmax-xmin)/num))\n",
    "    #print cox_velocity[counter], 'test'\n",
    "\n",
    "\n",
    "    t,tcox,tmix=tt,tt,tt\n",
    "    q1array = q(mixture)(xarray)\n",
    "    t,tcox,tmix=ttt,ttt,ttt\n",
    "    q2array = q(mixture)(xarray)\n",
    "    mixture_velocity[counter] = np.arccos(np.minimum(1,np.sum(q1array * q2array,dtype=np.double)*(xmax-xmin)/num))\n",
    "\n",
    "    t,tcox,tmix=tt,tt,tt\n",
    "    q1array = q(interpolant)(xarray)\n",
    "    t,tcox,tmix=ttt,ttt,ttt\n",
    "    q2array = q(interpolant)(xarray)\n",
    "    #print np.sum(q1array-q2array), 'check'\n",
    "    interpolant_velocity[counter] = np.arccos(np.minimum(1,np.sum(q1array * q2array,dtype=np.double)*(xmax-xmin)/num))\n",
    "    #print interpolant_velocity[counter], 'check'\n",
    "    counter=counter+1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-0.1, 0.1)"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
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      ],
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109d9bc90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(tarray,cox_velocity,c='r')\n",
    "plt.plot(tarray,mixture_velocity,c='g')\n",
    "plt.plot(tarray,interpolant_velocity, c='b')\n",
    "plt.ylim(-.1,.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}